Optimal. Leaf size=20 \[ -e^{4 e^2-x}+x+9 x^2 \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2194} \begin {gather*} 9 x^2+x-e^{4 e^2-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+9 x^2+\int e^{4 e^2-x} \, dx\\ &=-e^{4 e^2-x}+x+9 x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} -e^{4 e^2-x}+x+9 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 18, normalized size = 0.90 \begin {gather*} 9 \, x^{2} + x - e^{\left (-x + 4 \, e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.11, size = 18, normalized size = 0.90 \begin {gather*} 9 \, x^{2} + x - e^{\left (-x + 4 \, e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 19, normalized size = 0.95
method | result | size |
risch | \(x +9 x^{2}-{\mathrm e}^{4 \,{\mathrm e}^{2}-x}\) | \(19\) |
derivativedivides | \(x -{\mathrm e}^{4 \,{\mathrm e}^{2}} {\mathrm e}^{-x}+9 x^{2}\) | \(21\) |
default | \(x -{\mathrm e}^{4 \,{\mathrm e}^{2}} {\mathrm e}^{-x}+9 x^{2}\) | \(21\) |
norman | \(x -{\mathrm e}^{4 \,{\mathrm e}^{2}} {\mathrm e}^{-x}+9 x^{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 18, normalized size = 0.90 \begin {gather*} 9 \, x^{2} + x - e^{\left (-x + 4 \, e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 18, normalized size = 0.90 \begin {gather*} x-{\mathrm {e}}^{4\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-x}+9\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.75 \begin {gather*} 9 x^{2} + x - e^{- x} e^{4 e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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